I believe that when it comes to privacy and anonymity, you can't trust anyone at all. So what kind of information can a bitcoin mixer service get?
Yes, when privacy is the top priority you can't trust anyone, and thats people are advised to you 2 or more mixing services but there are some Bitcoin mixers that have been operating for years with no problem. The information the Bitcoin mixer gets is the wallet address used and IP address.
1) Mixer knows BTC address from which you send and knows the address to which you receive. Is information about the connection of the sending address with the receiving address saved? If this info is stored on their server, having access to this info, you can unravel the entire chain of transactions?
Yes, you're correct but there are some mixers that operated in p2p while there are some that provide you with a chip that is already funded before you mix your coin, and what they provide you is the chip that's equal to the amount of BTC want to receive with the private keys to the wallet that contain the Chips.
2) If the mixing service provider is a website, then it can get various information, such as an IP address and location? What can the mixer learn about its customers in this way?
You have already answered this question yourself but the last time I checked most Bitcoin mixers use Tor and what you need is to know how to use it. So, the IP address and user location shouldn't be a problem.
3) What information about users can generally be stored on bitcoin mixing service servers? If attackers / hackers get access to them, then this can be used to the detriment of users, right?
If the Bitcoin mixer uses Cloudflare they have enough information about their user saved. However, they didn't save any of their customer data theres information the hacker that access their website will get.
4) How can minimize the collection of personal information by mixers?
Every mixer has its own rules, regulations, and mode of operation. You just have to use those that have a good record and require minimum data.
5) What other weaknesses and vulnerabilities are there in the scheme "your address 1 - mixer - your address 2"?
Never mixer huge BTC, always use Tor, and make sure you use 3 direct mixing methods (decentralized mixing should be included).